1.) A random digit from 1 to 9 (inclusive) is chosen, with all digits being equally likely. The probability that when it's squared it will end with the digit 1.
2.) A random number between 1 and 20 (inclusive) is chosen. The probability that its square root will not be an integer.
probability - MathMate, Saturday, August 11, 2012 at 7:08am
1. Find how many (initial) digits when squared gives one. Dividing that by 9 will give you the required probability.
Also, it may be of interest to note that single digits that add up to 10 have the same last digits when squared.
Example: 2²=4 8²=(10-2)²=64 also ends with the digit 4.
2. Again, determine how many "perfect squares" there are among the numbers 1 to 20. Divide that number by 20 will give you the probability.